Hypothesis tests & confidence intervals worksheet with answers

Free printable Hypothesis tests & confidence intervals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
z −1.9601.96

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 12 mL. A sample of 25 bottles has a mean of 44.72 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 44.72 mLσ = 12 mLn = 25
z =
2.Easy
μ₀x̄c = ?α = 0.01

A supplier claims that the mean breaking strength of a cable is 500 kN; you suspect it is higher. The standard deviation is known to be 12 kN. You will take a sample of 25 cables and test H₀: μ = 500 kN against H₁: μ > 500 kN at α = 0.01. Above which sample mean x̄c will you reject H₀?

μ₀ = 500 kNσ = 12 kNn = 25α = 0.01
x̄c = kN
3.Medium
t −1.99801.998

A sample of 64 students has a mean score of 119.4 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 119.4s = 5n = 64
t =
4.Medium
−2.0932.093t = ?df = 19

Two teaching methods are compared. Group 1: 6 students, mean score 89.5, standard deviation 2.5. Group 2: 15 students, mean score 98.7, standard deviation 7. Assume equal population variances and use the pooled two-sample t test. Find the test statistic t for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (group 1 minus group 2).

n₁ = 6x̄₁ = 89.5s₁ = 2.5n₂ = 15x̄₂ = 98.7s₂ = 7
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 2α = 0.05βσ = 19, power 80%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 2 units with a power of 80%. The standard deviation is 19. Find the minimum sample size n.

α = 0.05power = 80%δ = 2σ = 19zα = 1.645zβ = 0.842
n =
6.Hard
−1.961.96z = ?

In a trial, 140 of 200 patients on treatment A recover, and 219 of 300 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 140n₁ = 200x₂ = 219n₂ = 300
z =

Answer key

  1. 1. z = −2.2
  2. 2. x̄c = 505.6 kN
  3. 3. t = −0.96
  4. 4. t = −3.1
  5. 5. n = 559
  6. 6. z = −0.7303

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